To center one object and rotate on another, choose the center object as the Focus Object in the Focus Object dialog box. Under View, choose "Rotating Frame Adjustment". Choose Ceres from the dropdown list. If Ceres drifts a bit, use the "Calibrate" button to fix. Click this button, click on Ceres' orbit. Wait a while, and click on Ceres' orbit again. This tells the program the rate of drift so it can compensate. The reason for the drift is it initially calculates Ceres' Period using Keplerian formulas that don't account for perturbations from other planets such as Jupiter.

I'm surprised that Ceres can have quasi-satellites, assuming that quasi-satellites are defined as being locked in resonance and librating about the 1:1 resonance. Ceres doesn't have much mass. An NBA basketball player could jump onto the roof of the arena if it were on Ceres.

From the reading I've done, Ceres, Vesta, and Pluto all have quasi-satellites, but in each of their cases, the orbital relationships are just coincidental, because of the low mass and gravity that they each have. Personally, I think that makes it more interesting. There's no reason it should be there, but yet, there it is.

Thanks for the help on the rotating frame. I'll try that out when I get a chance this evening.

Yes, you inspired a new sim! They're easy to make. With a little practice, you'll get good at making them. In the meantime, if there are any other asteroids (perhaps you'll email Wiegert et. al.), let me know and I'll make the sim for you, or teach you how to make them with their data. In the past, Wiegert has been very approachable and happy to answer emails.

A true quasi-satellite uses the planet's (in this case Ceres) gravity to stay locked in quasi-orbit for at least a few quasi orbits. This requires either a strong gravity or a VERY slow longitudinal approach. Ceres doesn't have strong gravity. Gefion has a very speedy longitudinal approach (apparent speed in the rotating frame). From everything I've seen, there's not a chance Ceres can capture Gefion. Haremari and Rentaro are amazingly still in the rotating frame, as Frank pointed out. That means they have almost the same semi-major axis, and hence orbital period as Ceres. But they will slowly drift. After centuries of approaching Ceres, Ceres might be able to influence their orbits. In the rotating frame, it can repel them. That would be a horseshoe or tadpole orbit. In a tadpole orbit, the object will also be seemingly repelled by Ceres' L3, while in a horseshoe orbit it will pass the L3 and centuries later approach Ceres from the other side. Ceres can also capture them into quasi-orbits. Or they can simply drift past Ceres after making a series of what seem like quasi-orbits. Only a simulation will tell.

Any object can have an "accidental" quasi satellite, even a massless object. It simply requires two objects very close to each other with the exact same semi-major axis and slightly different eccentricities. Imagine an astronaut untethered outside the ISS who fires a short blast of his thruster towards Earth. This does not change his semi-major axis. So he will still orbit the Earth with the exact same period as the space station. But the thrust introduced some eccentricity. He will drop closer to Earth, where he will speed up in orbit, allowing the ISS to get above and ahead of him in orbit. After he reaches perihelion, he'll climb again, this time slowing down in his orbit, allowing him to catch up to and surpass the ISS as he passes over it. To the astronaut, he is seemingly orbiting the ISS, yet it has nothing to do with the ISS's gravity.

A feature in the program that is useful for these types of sims is the "Auto Save" feature in the File menu. Set it to automatically save a copy of the sim every 100 years or so. That way when you wake in the morning to find that the asteroid in question has migrated past Ceres, you can "rewind" by opening the sim closest to the event.

Here is an animation of the above mentionned asteroids in rotating frame to Ceres , for the next 500 years . Each frame covers 4.6 years which is the orbital period of Ceres . It is remarkable how stable most orbits are , except for the apparental "breathing " which is probably due to disturbances from the nearby mighty Jupiter .

I took a look at the paper which was mentionned above ( Apostolos A. Christou, P. Wiegert ) . In this paper some asteroids are said to be in coorbital motion with Vesta : "22668","98231""156810","121118 ","134633"

The yellow one looks like it might actually be librating in a 1:1 with Ceres. The others seem to 'breathe' with the same period as each other, whether they're near Ceres or not, suggesting the Jupiter influence.

This suggests two more sims and animations: 1. Set Ceres mass to 0 and see if anything changes. 2. Set Jupiter's mass to 0 and see what changes.

Here's 2 more sims with all the asteroids you mentioned in your last 2 posts, so you or Scott can play around with them:

Here's an animation for 500 years of some of the asteroids , as an observer on the sun , looking at Ceres, would observe the coorbitals. Each frame covers 1 Ceres year . It is clear that the yellow asteroid does not "orbit" Ceres as is stays "under" the dwarf planet .

GravSim lets you output the screen under "File / Screenshots " . You then get a series of .bmp files , which can be converted by a gif animator program to an animated gif . This is done with free downloadable gif animator program .

The simulation hereunder extends the previous simulations. I could extend the number of coorbitals to 11 ( various sources ) . Further , the sim herunder covers 6000 years from now. It is amazing how different the orbits of each coorbital behave .

I wouldn't think so , see the animation hereunder which spans 6000 years . The orbits of each coorbital show at first sight no real correlation, except for the SMA which is close to Ceres" SMA.

Ceres is represented in blue . The coorbitals are represented in different colors . Remarkable is the strong precession of the orbits ( due to the overall precession of of solar system , for whick Jupiter and Saturn are responsable ..among others )